Problem: Find the distance between the points (0,4) and (3,0).
Explanation: We use the distance formula: $\sqrt{(3 - 0)^2 + (0 - 4)^2} = \sqrt{9 + 16} = \boxed{5}$.

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We note that the points $(0, 4)$, $(3, 0)$, and $(0, 0)$ form a right triangle with legs of length 3 and 4. This is a Pythagorean triple, so the hypotenuse must have length $\boxed{5}$.